EXTENSION OF XENON OSCILLATIONS SAFETY MARGINS USING WEAKLY NONLINEAR STABILITY ANALYSIS

Weakly nonlinear stability analysis is applied to study xenon oscillations in nuclear reactors using the approach of multiple time-scales method. This approach allows to characterize the dynamics of the system beyond the Hopf instability point. It provides important insight on the characteristics of the oscillations, namely if they diverge with time, or converge into a bounded limit cycle. Detailed derivation of the amplitude equation is presented. This equation is used to identify parameter ranges of bounded periodic oscillations, which may be allowed for safe operation. The influence of neutron generation time and the power feedback coefficients on the amplitude of limit cycles, as well as on convergence times, is discussed. The described method may be used to extend the safety margins required to prevent xenon unstable oscillations in reactor cores.